Acyclic Edge Coloring of Triangle-Free Toroidal Graphs

Abstract

A proper edge coloring \(c\) of a graph \(G\) is said to be acyclic if \(G\) has no bicolored cycle with respect to \(c\). It is proved that every triangle-free toroidal graph \(G\) admits an acyclic edge coloring with \((\Delta(G) + 5)\) colors. This generalizes a theorem from \([8]\).